Throughout the current campaign, the Belgian duo have both been linked with a summer switch to Real Madrid but Chelsea have suggested that they remain confident of keeping the pair at the club for at least another season.
However, according to The Mirror, the Blues are bracing themselves for concrete approaches from elsewhere, with Paris Saint-Germain also said to be keeping an eye on any developments.
Hazard has just over two years remaining on his contract, but Courtois has less than 15 months and Chelsea's hand could be forced if the goalkeeper does not show a willingness to pen fresh terms.
In midweek, Chelsea were eliminated from the Champions League and if the club do no qualify for next season's competition through the Premier League, the West Londoners face a summer of upheaval.
Strong doubts also remain over the future of head coach Antonio Conte, with reports continuing to suggest that the Italian will move on before the start of the next campaign.